A control system for a perfusion system (1), the control system being configured to control a plurality of blood flow rates in the perfusion system during a weaning phase. The perfusion system comprises: a first blood line (26) in which blood is permitted to flow at a first flow rate; a second blood line (34) in which blood is permitted to flow at a second flow rate; an arterial blood line (22) in which blood is permitted to flow at an arterial flow rate; and an arterial pump (20) configured to circulate blood at the arterial flow rate in the arterial blood line. The control system comprises a controller configured to determine the first flow rate and the second flow rate and to process the first and second flow rates to determine a desired arterial flow rate. The controller is configured to operate in a first mode in which the controller modulates operation of the arterial pump (20) to adjust the arterial flow rate so that the arterial flow rate matches the desired arterial flow rate.